// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_HYPERPLANE_H
#define EIGEN_HYPERPLANE_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
  *
  * \class Hyperplane
  *
  * \brief A hyperplane
  *
  * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
  * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
  *
  * \tparam _Scalar the scalar type, i.e., the type of the coefficients
  * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
  *             Notice that the dimension of the hyperplane is _AmbientDim-1.
  *
  * This class represents an hyperplane as the zero set of the implicit equation
  * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
  * and \f$ d \f$ is the distance (offset) to the origin.
  */
template <typename _Scalar, int _AmbientDim, int _Options> class Hyperplane
{
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar, _AmbientDim == Dynamic ? Dynamic : _AmbientDim + 1)
    enum
    {
        AmbientDimAtCompileTime = _AmbientDim,
        Options = _Options
    };
    typedef _Scalar Scalar;
    typedef typename NumTraits<Scalar>::Real RealScalar;
    typedef Eigen::Index Index;  ///< \deprecated since Eigen 3.3
    typedef Matrix<Scalar, AmbientDimAtCompileTime, 1> VectorType;
    typedef Matrix<Scalar, Index(AmbientDimAtCompileTime) == Dynamic ? Dynamic : Index(AmbientDimAtCompileTime) + 1, 1, Options> Coefficients;
    typedef Block<Coefficients, AmbientDimAtCompileTime, 1> NormalReturnType;
    typedef const Block<const Coefficients, AmbientDimAtCompileTime, 1> ConstNormalReturnType;

    /** Default constructor without initialization */
    EIGEN_DEVICE_FUNC inline Hyperplane() {}

    template <int OtherOptions> EIGEN_DEVICE_FUNC Hyperplane(const Hyperplane<Scalar, AmbientDimAtCompileTime, OtherOptions>& other) : m_coeffs(other.coeffs())
    {
    }

    /** Constructs a dynamic-size hyperplane with \a _dim the dimension
    * of the ambient space */
    EIGEN_DEVICE_FUNC inline explicit Hyperplane(Index _dim) : m_coeffs(_dim + 1) {}

    /** Construct a plane from its normal \a n and a point \a e onto the plane.
    * \warning the vector normal is assumed to be normalized.
    */
    EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const VectorType& e) : m_coeffs(n.size() + 1)
    {
        normal() = n;
        offset() = -n.dot(e);
    }

    /** Constructs a plane from its normal \a n and distance to the origin \a d
    * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
    * \warning the vector normal is assumed to be normalized.
    */
    EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const Scalar& d) : m_coeffs(n.size() + 1)
    {
        normal() = n;
        offset() = d;
    }

    /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
    * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
    */
    EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
    {
        Hyperplane result(p0.size());
        result.normal() = (p1 - p0).unitOrthogonal();
        result.offset() = -p0.dot(result.normal());
        return result;
    }

    /** Constructs a hyperplane passing through the three points. The dimension of the ambient space
    * is required to be exactly 3.
    */
    EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
    {
        EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
        Hyperplane result(p0.size());
        VectorType v0(p2 - p0), v1(p1 - p0);
        result.normal() = v0.cross(v1);
        RealScalar norm = result.normal().norm();
        if (norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon())
        {
            Matrix<Scalar, 2, 3> m;
            m << v0.transpose(), v1.transpose();
            JacobiSVD<Matrix<Scalar, 2, 3>> svd(m, ComputeFullV);
            result.normal() = svd.matrixV().col(2);
        }
        else
            result.normal() /= norm;
        result.offset() = -p0.dot(result.normal());
        return result;
    }

    /** Constructs a hyperplane passing through the parametrized line \a parametrized.
    * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
    * so an arbitrary choice is made.
    */
    // FIXME to be consistent with the rest this could be implemented as a static Through function ??
    EIGEN_DEVICE_FUNC explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
    {
        normal() = parametrized.direction().unitOrthogonal();
        offset() = -parametrized.origin().dot(normal());
    }

    EIGEN_DEVICE_FUNC ~Hyperplane() {}

    /** \returns the dimension in which the plane holds */
    EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime == Dynamic ? m_coeffs.size() - 1 : Index(AmbientDimAtCompileTime); }

    /** normalizes \c *this */
    EIGEN_DEVICE_FUNC void normalize(void) { m_coeffs /= normal().norm(); }

    /** \returns the signed distance between the plane \c *this and a point \a p.
    * \sa absDistance()
    */
    EIGEN_DEVICE_FUNC inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }

    /** \returns the absolute distance between the plane \c *this and a point \a p.
    * \sa signedDistance()
    */
    EIGEN_DEVICE_FUNC inline Scalar absDistance(const VectorType& p) const { return numext::abs(signedDistance(p)); }

    /** \returns the projection of a point \a p onto the plane \c *this.
    */
    EIGEN_DEVICE_FUNC inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }

    /** \returns a constant reference to the unit normal vector of the plane, which corresponds
    * to the linear part of the implicit equation.
    */
    EIGEN_DEVICE_FUNC inline ConstNormalReturnType normal() const { return ConstNormalReturnType(m_coeffs, 0, 0, dim(), 1); }

    /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
    * to the linear part of the implicit equation.
    */
    EIGEN_DEVICE_FUNC inline NormalReturnType normal() { return NormalReturnType(m_coeffs, 0, 0, dim(), 1); }

    /** \returns the distance to the origin, which is also the "constant term" of the implicit equation
    * \warning the vector normal is assumed to be normalized.
    */
    EIGEN_DEVICE_FUNC inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }

    /** \returns a non-constant reference to the distance to the origin, which is also the constant part
    * of the implicit equation */
    EIGEN_DEVICE_FUNC inline Scalar& offset() { return m_coeffs(dim()); }

    /** \returns a constant reference to the coefficients c_i of the plane equation:
    * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
    */
    EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }

    /** \returns a non-constant reference to the coefficients c_i of the plane equation:
    * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
    */
    EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }

    /** \returns the intersection of *this with \a other.
    *
    * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
    *
    * \note If \a other is approximately parallel to *this, this method will return any point on *this.
    */
    EIGEN_DEVICE_FUNC VectorType intersection(const Hyperplane& other) const
    {
        EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
        Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
        // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
        // whether the two lines are approximately parallel.
        if (internal::isMuchSmallerThan(det, Scalar(1)))
        {  // special case where the two lines are approximately parallel. Pick any point on the first line.
            if (numext::abs(coeffs().coeff(1)) > numext::abs(coeffs().coeff(0)))
                return VectorType(coeffs().coeff(1), -coeffs().coeff(2) / coeffs().coeff(1) - coeffs().coeff(0));
            else
                return VectorType(-coeffs().coeff(2) / coeffs().coeff(0) - coeffs().coeff(1), coeffs().coeff(0));
        }
        else
        {  // general case
            Scalar invdet = Scalar(1) / det;
            return VectorType(invdet * (coeffs().coeff(1) * other.coeffs().coeff(2) - other.coeffs().coeff(1) * coeffs().coeff(2)),
                              invdet * (other.coeffs().coeff(0) * coeffs().coeff(2) - coeffs().coeff(0) * other.coeffs().coeff(2)));
        }
    }

    /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
    *
    * \param mat the Dim x Dim transformation matrix
    * \param traits specifies whether the matrix \a mat represents an #Isometry
    *               or a more generic #Affine transformation. The default is #Affine.
    */
    template <typename XprType> EIGEN_DEVICE_FUNC inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
    {
        if (traits == Affine)
        {
            normal() = mat.inverse().transpose() * normal();
            m_coeffs /= normal().norm();
        }
        else if (traits == Isometry)
            normal() = mat * normal();
        else
        {
            eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
        }
        return *this;
    }

    /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
    *
    * \param t the transformation of dimension Dim
    * \param traits specifies whether the transformation \a t represents an #Isometry
    *               or a more generic #Affine transformation. The default is #Affine.
    *               Other kind of transformations are not supported.
    */
    template <int TrOptions>
    EIGEN_DEVICE_FUNC inline Hyperplane& transform(const Transform<Scalar, AmbientDimAtCompileTime, Affine, TrOptions>& t, TransformTraits traits = Affine)
    {
        transform(t.linear(), traits);
        offset() -= normal().dot(t.translation());
        return *this;
    }

    /** \returns \c *this with scalar type casted to \a NewScalarType
    *
    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
    * then this function smartly returns a const reference to \c *this.
    */
    template <typename NewScalarType>
    EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Hyperplane, Hyperplane<NewScalarType, AmbientDimAtCompileTime, Options>>::type cast() const
    {
        return typename internal::cast_return_type<Hyperplane, Hyperplane<NewScalarType, AmbientDimAtCompileTime, Options>>::type(*this);
    }

    /** Copy constructor with scalar type conversion */
    template <typename OtherScalarType, int OtherOptions>
    EIGEN_DEVICE_FUNC inline explicit Hyperplane(const Hyperplane<OtherScalarType, AmbientDimAtCompileTime, OtherOptions>& other)
    {
        m_coeffs = other.coeffs().template cast<Scalar>();
    }

    /** \returns \c true if \c *this is approximately equal to \a other, within the precision
    * determined by \a prec.
    *
    * \sa MatrixBase::isApprox() */
    template <int OtherOptions>
    EIGEN_DEVICE_FUNC bool isApprox(const Hyperplane<Scalar, AmbientDimAtCompileTime, OtherOptions>& other,
                                    const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
    {
        return m_coeffs.isApprox(other.m_coeffs, prec);
    }

protected:
    Coefficients m_coeffs;
};

}  // end namespace Eigen

#endif  // EIGEN_HYPERPLANE_H
